The two current answers both focus on paragraph styles (the only kind of "styles" search available from CTRL-H, I believe).

If you want to select character styles (e.g., change all bold to underline for example), then you probably need the the Extended Search/Replace extension. There's a step-by-step guide in another Q&A to using it to replace paragraph styles (and see this related one, too), but it can also replace character styles (you might want/need to set up some new custom ones).

It's certainly worth experimenting with, as it is a very powerful tool for manipulating the text.